Paul Nylander’s World of 3D Printed Math Art

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Gee! We humans sure are getting smart! Or, at the very least, our software is. With powerful minds and powerful programs, a new category of art, dubbed Math Art, has sprung up all over the Internet. New software has allowed artists to generate interesting and mesmerizing patterns using complex algorithms and geometries. To partner with this software and to bring those interesting shapes into the third dimension is our favourite technology, 3D printing. At the 3D Printer World Expo this past weekend, we got to lay our eyes on the work of Paul Nylander, who uses a variety of math procedures to generate beautiful 3D printed artwork.

The object drawing attention to Paul’s work was the 8-inch Loxodrome Lamp, which illuminated a double spiral of light onto the wall using stereographic projection. The lamp achieves a beautiful effect, but I wondered where the name came from. As Paul explained it,

The loxodrome is a nautical term referring to the path that a ship follows on the Earth if it maintains a constant heading. For example, if a ship maintains a heading of 45° North-East, then it will spiral around the North pole as it approaches the pole, but it will never reach the North pole because it is not pointing due North. Similarly, the ship will spiral around the South pole in the opposite direction if it follows the path in reverse.

As it turns out, this wasn’t the artist’s first venture into 3D printing. After getting back home, I checked out his website to find a huge array of 3D printed works derived from mathematical principles. For instance, Paul created a number of geodesics made up of varying degrees of knottiness. The 3D printed balls covered in braids, weaves and rings may be ideal for Christmas ornaments or decorative lighting, as Paul suggests that a small LED turns them into wonderful, glowing lights.

Bugman, as he’s called on Shapeways, also designed this 3D printed rose by plotting “a single, continuous, parametric math equation,” saying, “I got this idea while trying to create a visualization of a spiraling spin-lattice relaxation for a physics experiment involving a Nuclear Magnetic Resonance (NMR) spectrometer.” If that’s too organic for you, you might try out his insane Knotted Gear lamp, which is made up of 92 interlocking and moveable gears.

For some of his designs, he actually lists the Mathematica formula. If you download Mathematica, you can take some of his 3D renderings and try to produce .stl files for yourself. Otherwise, you can head over to his Shapeways page and purchase them. Unfortunately, the Knotted Gear lamp and the Loxodrome Lamp are not on sale, yet, but Paul implies that they will be in the coming days, thanks to the great deal of interest he experienced at the Expo.

Michael Molitch-Hou previously served as Editor-in-Chief of 3D Printing Industry, he is now the Editor of Engineering . com's 3D printing section. He has covered additive manufacturing technology day in and day out since 2012 and has hundreds of article to his credit. He is the founder of The Reality Institute.